Merge branch 'master' into UpToDate

thofma · Dec 7, 2023 · 7f61466 · 7f61466
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diff --git a/Project.toml b/Project.toml
@@ -1,6 +1,6 @@
 name = "Hecke"
 uuid = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
-version = "0.22.8"
+version = "0.23.0"
 
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
@@ -28,7 +28,7 @@ GAPExt = "GAP"
 PolymakeExt = "Polymake"
 
 [compat]
-AbstractAlgebra = "0.34"
+AbstractAlgebra = "^0.34.4"
 Dates = "1.6"
 Distributed = "1.6"
 GAP = "0.9.6, 0.10"
@@ -37,7 +37,7 @@ LazyArtifacts = "1.6"
 Libdl = "1.6"
 LinearAlgebra = "1.6"
 Markdown = "1.6"
-Nemo = "0.38"
+Nemo = "^0.38.2"
 Pkg = "1.6"
 Polymake = "0.10, 0.11"
 Printf = "1.6"

diff --git a/README.md b/README.md
@@ -69,28 +69,32 @@ Here is a quick example of using Hecke:
 
 ```julia
 julia> using Hecke
-...
 
 Welcome to
 
-  _    _           _
- | |  | |         | |
- | |__| | ___  ___| | _____
- |  __  |/ _ \/ __| |/ / _ \
- | |  | |  __/ (__|   <  __/
- |_|  |_|\___|\___|_|\_\___|
+    _    _           _
+   | |  | |         | |
+   | |__| | ___  ___| | _____
+   |  __  |/ _ \/ __| |/ / _ \
+   | |  | |  __/ (__|   <  __/
+   |_|  |_|\___|\___|_|\_\___|
+
+Version 0.22.8...
+ ... which comes with absolutely no warranty whatsoever
+(c) 2015-2023 by Claus Fieker, Tommy Hofmann and Carlo Sircana
 
-Version 0.10.12...
- ... which comes with absolutely no warrant whatsoever
-(c) 2015-2019 by Claus Fieker, Tommy Hofmann and Carlo Sircana
 
 julia> Qx, x = polynomial_ring(FlintQQ, "x");
+
 julia> f = x^3 + 2;
+
 julia> K, a = number_field(f, "a");
+
 julia> O = maximal_order(K);
+
 julia> O
-Maximal order of Number field over Rational Field with defining polynomial x^3 + 2
-with basis [1,a,a^2]
+Maximal order of Number field of degree 3 over QQ
+with basis nf_elem[1, a, a^2]
 ```
 
 ## Documentation

diff --git a/docs/mkdocs.yml b/docs/mkdocs.yml
@@ -114,6 +114,7 @@ nav:
       - Misc: misc.md
     - Extra features:
       - Macros: features/macros.md
+      - Multi-sets: features/mset.md
     - References: 'references.md'
     - Examples: 'examples.md'
     - Developer:

diff --git a/docs/src/index.md b/docs/src/index.md
@@ -42,40 +42,48 @@ Here is a quick example of using Hecke:
 
 ```julia
 julia> using Hecke
-...
 
 Welcome to
 
-  _    _           _
- | |  | |         | |
- | |__| | ___  ___| | _____
- |  __  |/ _ \/ __| |/ / _ \
- | |  | |  __/ (__|   <  __/
- |_|  |_|\___|\___|_|\_\___|
+    _    _           _
+   | |  | |         | |
+   | |__| | ___  ___| | _____
+   |  __  |/ _ \/ __| |/ / _ \
+   | |  | |  __/ (__|   <  __/
+   |_|  |_|\___|\___|_|\_\___|
 
-Version 0.9.0 ...
+Version 0.22.8...
  ... which comes with absolutely no warranty whatsoever
-(c) 2015-2018 by Claus Fieker, Tommy Hofmann and Carlo Sircana
+(c) 2015-2023 by Claus Fieker, Tommy Hofmann and Carlo Sircana
+
 
 julia> Qx, x = polynomial_ring(FlintQQ, "x");
+
 julia> f = x^3 + 2;
+
 julia> K, a = number_field(f, "a");
+
 julia> O = maximal_order(K);
+
 julia> O
-Maximal order of Number field over Rational Field with defining polynomial x^3 + 2
-with basis [1,a,a^2]
+Maximal order of Number field of degree 3 over QQ
+with basis nf_elem[1, a, a^2]
 ```
 
 The documentation of the single functions can also be accessed at the julia prompt. Here is an example:
 
 ```
-help?> signature
-search: signature
+help?> absolute_degree
+search: absolute_degree absolute_inertia_degree absolute_coordinates is_absolutely_irreducible
+
+  absolute_degree(a::FqField)
+
+  Return the degree of the given finite field over the prime field.
 
-  ----------------------------------------------------------------------------
+  ─────────────────────────────────────────────────────────────────────────────────────────────────
 
-  signature(O::NfMaximalOrder) -> Tuple{Int, Int}
+  absolute_degree(L::NumField) -> Int
 
-  |  Returns the signature of the ambient number field of \mathcal O.
+  Given a number field L/K, this function returns the degree of L over \mathbf Q.
 ```
 
diff --git a/docs/src/quad_forms/basics.md b/docs/src/quad_forms/basics.md
@@ -21,7 +21,7 @@ following spaces for the rest of this section:
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(7);
+K, a = cyclotomic_real_subfield(7);
 Kt, t = K["t"];
 E, b = number_field(t^2-a*t+1, "b");
 Q = quadratic_space(K, K[0 1; 1 0])
@@ -59,7 +59,7 @@ space $H$:
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(7);
+K, a = cyclotomic_real_subfield(7);
 Kt, t = K["t"];
 E, b = number_field(t^2-a*t+1, "b");
 H = hermitian_space(E, 3);
@@ -96,7 +96,7 @@ Note that the `is_hermitian` function tests whether the space is non-quadratic.
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(7);
+K, a = cyclotomic_real_subfield(7);
 Kt, t = K["t"];
 E, b = number_field(t^2-a*t+1, "b");
 Q = quadratic_space(K, K[0 1; 1 0]);
@@ -123,7 +123,7 @@ restrict_scalars(::AbstractSpace, ::QQField, ::FieldElem)
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(7);
+K, a = cyclotomic_real_subfield(7);
 Kt, t = K["t"];
 E, b = number_field(t^2-a*t+1, "b");
 Q = quadratic_space(K, K[0 1; 1 0]);
@@ -160,7 +160,7 @@ of $O_K$ above $7$, one can get:
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(7);
+K, a = cyclotomic_real_subfield(7);
 Q = quadratic_space(K, K[0 1; 1 0]);
 OK = maximal_order(K);
 p = prime_decomposition(OK, 7)[1][1];
@@ -196,7 +196,7 @@ embed respectively locally or globally into $Q$ or $H$:
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(7);
+K, a = cyclotomic_real_subfield(7);
 Kt, t = K["t"];
 E, b = number_field(t^2-a*t+1, "b");
 Q = quadratic_space(K, K[0 1; 1 0]);
@@ -247,7 +247,7 @@ orthogonal_projection(::AbstractSpace, ::MatElem)
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(7);
+K, a = cyclotomic_real_subfield(7);
 Kt, t = K["t"];
 Q = quadratic_space(K, K[0 1; 1 0]);
 orthogonal_complement(Q, matrix(K, 1, 2, [1 0]))
@@ -268,7 +268,7 @@ is_isotropic(::AbstractSpace, p)
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(7);
+K, a = cyclotomic_real_subfield(7);
 Kt, t = K["t"];
 E, b = number_field(t^2-a*t+1, "b");
 H = hermitian_space(E, 3);
@@ -295,7 +295,7 @@ is_locally_hyperbolic(::HermSpace, ::NfOrdIdl)
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(7);
+K, a = cyclotomic_real_subfield(7);
 Kt, t = K["t"];
 E, b = number_field(t^2-a*t+1, "b");
 H = hermitian_space(E, 3);

diff --git a/docs/src/quad_forms/genusherm.md b/docs/src/quad_forms/genusherm.md
@@ -473,7 +473,7 @@ hermitian_genera(::Hecke.NfRel, ::Int, ::Dict{InfPlc, Int}, ::Union{Hecke.NfRelO
 
 ```@repl 2
 using Hecke # hide
-K, a = CyclotomicRealSubfield(8, "a");
+K, a = cyclotomic_real_subfield(8, "a");
 Kt, t = K["t"];
 E, b = number_field(t^2 - a * t + 1);
 p = prime_decomposition(maximal_order(K), 2)[1][1];

diff --git a/examples/NFDB.jl b/examples/NFDB.jl
@@ -1175,9 +1175,10 @@ function _p_adic_regulator(K, p)
     end
     C, mC = completion(K, P, prec)
     Rmat = zero_matrix(C, r, r)
+    D = Dict{nf_elem, LocalFieldElem{qadic, EisensteinLocalField}}()
     for i in 1:r
       for j in 1:r
-        Rmat[i, j] = _evaluate_log_of_fac_elem(mC, P, mA(A[i])(mU(U[j + 1]))) # j + 1, because the fundamental units correspond to U[2],..,U[r + 1]
+        Rmat[i, j] = _evaluate_log_of_fac_elem(mC, P, mA(A[i])(mU(U[j + 1])), D) # j + 1, because the fundamental units correspond to U[2],..,U[r + 1]
       end
     end
     z = _det(Rmat)
@@ -1189,14 +1190,26 @@ function _p_adic_regulator(K, p)
   end
 end
 
-function _evaluate_log_of_fac_elem(mC, P, e)
+function _evaluate_log_of_fac_elem(mC, P, e::FacElem{nf_elem, AnticNumberField}, D = Dict{nf_elem, LocalFieldElem{qadic, EisensteinLocalField}}())
   C = codomain(mC)
   K = base_ring(e)
   pi = K(uniformizer(P))
-  # at the moment log() works only for valuation == 0,
+  # We want to compute
+  # sum(n * log(mC(pi^(-valuation(b, P)) * b)) for (b, n) in e; init = zero(C))
+  # but we cache the result of the individual log(), since the elements we look
+  # at have large intersection for their bases.
+  #
+  # At the moment log() works only for valuation == 0,
   # but since we have a unit, we can just scale in every factor
-  l = sum(n * log(mC(pi^(-valuation(b, P)) * b)) for (b, n) in e; init = zero(C))
-  return l
+  res = zero(C)
+  for (b, n) in e
+    l = get!(D, b) do
+      bb = mC(pi^(-valuation(b, P)) * b)
+      return log(bb)
+    end
+    res = res + n * l
+  end
+  return res
 end
 
 function _padic_regulator_non_normal(K, p)

diff --git a/src/AlgAss/AlgMat.jl b/src/AlgAss/AlgMat.jl
@@ -18,8 +18,6 @@ basis(A::AlgMat) = A.basis
 
 has_one(A::AlgMat) = true
 
-elem_type(A::AlgMat{T, S}) where { T, S } = AlgMatElem{T, AlgMat{T, S}, S}
-
 elem_type(::Type{AlgMat{T, S}}) where { T, S } = AlgMatElem{T, AlgMat{T, S}, S}
 
 order_type(::AlgMat{QQFieldElem, S}) where { S } = AlgAssAbsOrd{AlgMat{QQFieldElem, S}, elem_type(AlgMat{QQFieldElem, S})}

diff --git a/src/AlgAss/AlgQuat.jl b/src/AlgAss/AlgQuat.jl
@@ -53,8 +53,6 @@ standard_form(A::AlgQuat) = A.std
 
 has_one(A::AlgQuat) = true
 
-elem_type(A::AlgQuat{T}) where {T} = AlgAssElem{T, AlgQuat{T}}
-
 elem_type(::Type{AlgQuat{T}}) where {T} = AlgAssElem{T, AlgQuat{T}}
 
 is_commutative(A::AlgQuat) = false

diff --git a/src/AlgAssAbsOrd/Elem.jl b/src/AlgAssAbsOrd/Elem.jl
@@ -2,8 +2,6 @@ export elem_in_algebra
 
 parent_type(::Type{AlgAssAbsOrdElem{S, T}}) where {S, T} = AlgAssAbsOrd{S, T}
 
-parent_type(::AlgAssAbsOrdElem{S, T}) where {S, T} = AlgAssAbsOrd{S, T}
-
 @inline parent(x::AlgAssAbsOrdElem) = x.parent
 
 Base.hash(x::AlgAssAbsOrdElem, h::UInt) = hash(elem_in_algebra(x, copy = false), h)

diff --git a/src/AlgAssAbsOrd/Ideal.jl b/src/AlgAssAbsOrd/Ideal.jl
@@ -1447,8 +1447,6 @@ FracIdealSet(O::AlgAssAbsOrd) = IdealSet(O)
 
 elem_type(::Type{AlgAssAbsOrdIdlSet{S, T}}) where {S, T} = AlgAssAbsOrdIdl{S, T}
 
-elem_type(::AlgAssAbsOrdIdlSet{S, T}) where {S, T} = AlgAssAbsOrdIdl{S, T}
-
 parent_type(::Type{AlgAssAbsOrdIdl{S, T}}) where {S, T} = AlgAssAbsOrdIdlSet{S, T}
 
 function Base.one(S::AlgAssAbsOrdIdlSet)

diff --git a/src/AlgAssAbsOrd/Order.jl b/src/AlgAssAbsOrd/Order.jl
@@ -1,10 +1,8 @@
-export algebra, integral_group_ring
+export algebra, ideal_type, integral_group_ring
 
 add_assertion_scope(:AlgAssOrd)
 add_verbosity_scope(:AlgAssOrd)
 
-elem_type(::AlgAssAbsOrd{S, T}) where {S, T} = AlgAssAbsOrdElem{S, T}
-
 elem_type(::Type{AlgAssAbsOrd{S, T}}) where {S, T} = AlgAssAbsOrdElem{S, T}
 
 ideal_type(::AlgAssAbsOrd{S, T}) where {S, T} = AlgAssAbsOrdIdl{S, T}

diff --git a/src/AlgAssRelOrd/Elem.jl b/src/AlgAssRelOrd/Elem.jl
@@ -4,8 +4,6 @@ export trred
 
 parent_type(::Type{AlgAssRelOrdElem{S, T, U}}) where {S, T, U} = AlgAssRelOrd{S, T, U}
 
-parent_type(::AlgAssRelOrdElem{S, T, U}) where {S, T, U} = AlgAssRelOrd{S, T, U}
-
 @doc raw"""
     parent(x::AlgAssRelOrdElem) -> AlgAssRelOrd
 

diff --git a/src/AlgAssRelOrd/Order.jl b/src/AlgAssRelOrd/Order.jl
@@ -1,6 +1,4 @@
-export is_commutative, trred_matrix, any_order, pmaximal_overorder, phereditary_overorder, is_maximal
-
-elem_type(::AlgAssRelOrd{S, T, U}) where {S, T, U} = AlgAssRelOrdElem{S, T, U}
+export is_commutative, trred_matrix, any_order, pmaximal_overorder, phereditary_overorder, is_maximal, ideal_type
 
 elem_type(::Type{AlgAssRelOrd{S, T, U}}) where {S, T, U} = AlgAssRelOrdElem{S, T, U}
 

diff --git a/src/EllCrv/EllCrv.jl b/src/EllCrv/EllCrv.jl
@@ -775,10 +775,6 @@ end
 #
 ################################################################################
 
-function elem_type(E::EllCrv{T}) where T
-  return EllCrvPt{T}
-end
-
 function elem_type(::Type{EllCrv{T}}) where T
   return EllCrvPt{T}
 end

diff --git a/src/FunField/HessQR.jl b/src/FunField/HessQR.jl
@@ -143,9 +143,7 @@ function Hecke.denominator(a::Generic.RationalFunctionFieldElem, S::HessQR)
   return integral_split(a, S)[2]
 end
 
-Nemo.elem_type(::HessQR) = HessQRElem
 Nemo.elem_type(::Type{HessQR}) = HessQRElem
-Nemo.parent_type(::HessQRElem) = HessQR
 Nemo.parent_type(::Type{HessQRElem}) = HessQR
 Nemo.is_domain_type(::Type{HessQRElem}) = true
 

diff --git a/src/GenOrd/GenOrd.jl b/src/GenOrd/GenOrd.jl
@@ -46,14 +46,10 @@ function elem_type(::Type{GenOrd{S, T}}) where {S, T}
   return GenOrdElem{elem_type(S), elem_type(T)}
 end
 
-elem_type(::O) where {O <: GenOrd} = elem_type(O)
-
 function parent_type(::Type{GenOrdElem{S, T}}) where {S, T}
   return GenOrd{parent_type(S), parent_type(T)}
 end
 
-parent_type(::OE) where {OE <: GenOrdElem} = parent_type(OE)
-
 # prepare for algebras, which are not domains
 is_domain_type(::Type{GenOrdElem{S, T}}) where {S, T} = is_domain_type(S)
 

diff --git a/src/Grp/GenGrp.jl b/src/Grp/GenGrp.jl
@@ -181,8 +181,6 @@ end
 
 elem_type(::Type{GrpGen}) = GrpGenElem
 
-elem_type(::GrpGen) = GrpGenElem
-
 Base.hash(G::GrpGenElem, h::UInt) = Base.hash(G.i, h)
 
 Base.hash(G::GrpGen, h::UInt) = UInt(0)